Find V0...

What I've tried

Assuming current goes around outer loop counter-clockwise:

Where i1 is current at 4 Ohm resistor: \(V_0 = -4 \cdot i_1\)
(I believe there should be a negative sign there because the assumed current is going from - to + across the resistor)

Using KVL around outer loop going counter-clockwise:
\(2 \cdot V_0 - 4 \cdot i_1 - 6 \cdot i_1 = 0\)
\(V_0 = 5 \cdot i_1\)

Clearly, these two formulas don't agree. Can someone explain what I am doing wrong? I've really been wringing my hands over this one. Thanks!

 

The 2*V0 denotes the current through the element, not the voltage across it. Hence, your KVL equation is incorrect.

 

The current source on the right is a dependent current source with is value equal to 2*Vo. You have to include this in your KCL.

 

The 2*V0 denotes the current through the element, not the voltage across it. Hence, your KVL equation is incorrect.

Thanks!

I knew the symbol was a dependent current source, but I would never have guessed that the 2*V0 was a current value rather than a voltage value... With that, the problem is solvable. Thanks!

i = 10/9 A
V0 = -40/9 V

 

So when a digram shows a current source with a label like 2*V, that's a current value.
And when a diagram shows a voltage source with a label like 2*i, that's a voltage value.

I literally spent about 5-6 hours on a few problems where I was making the exact same mistake... Thanks again!

 

So when a digram shows a current source with a label like 2*V, that's a current value.
And when a diagram shows a voltage source with a label like 2*i, that's a voltage value.

I literally spent about 5-6 hours on a few problems where I was making the exact same mistake... Thanks again!

It doesn't mean that 2*i and 2*v is always voltage and current respecticely. 2*i and 2*v just shoes the value of the current or voltage. If it is current or voltage depends on the symbol in the schematic.

 

So when a digram shows a current source with a label like 2*V, that's a current value.
And when a diagram shows a voltage source with a label like 2*i, that's a voltage value.

I literally spent about 5-6 hours on a few problems where I was making the exact same mistake... Thanks again!

The various common dependent sources come in 4 flavors.

1. current controlled current source.
2. current controlled voltage source.
3. voltage controlled voltage source.
4. voltage controller current source.

Each of these have their on unique schematic symbol.

The dependent source in your problem is of the voltage controlled current source type.

hgmjr

 

Thanks!

I knew the symbol was a dependent current source, but I would never have guessed that the 2*V0 was a current value rather than a voltage value... With that, the problem is solvable. Thanks!

i = 10/9 A
V0 = -40/9 V

These are the same answers I obtained.

hgmjr